If you mean:
Yes. There are various ways to stop it. For the first slideshow you can do:
Which can be restarted by moving the mouse over and out of the slideshow, or by doing:
For a more permanent stop (a mouse over/out cannot restart it after this):
To restart after that:
and as long as the cycles set in the init haven't run out, and the slideshow's setting.displaymode.type hasn't been switched away from 'auto', it will restart. If it has done either of those things though, it can be reset. If this is your intent though, best to set the cycles to 0 in the init, which is infinite. Then all you have to do to ensure it will restart is:
As for switching back and forth among various slideshows, that also can be done in various ways. I'm not sure what you mean about the close button. Do you mean get rid of all the slideshows, or just one at a time? Either way, perhaps the easiest way would to be to put each slideshow on a separate page, and switch between them via loading one individual of these pages into an iframe on your main page for this.
translideshow1.displaymode.type = 'auto'; translideshow1.rotate();